• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.431-449
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• 2017

Acute triangles and obtuse triangles are defined according to the classification of triangles by angles. The definitions of acute triangles and obtuse triangles are difficult for students because they are related to different logical elements. The purpose of this study is to seek desirable methods for teaching the classification of triangles by angles related to logic. To do this, based on the theoretical consideration and the longitudinal analysis of the elementary mathematics textbooks, some implications are found for teaching. And then the lesson was planned and applied to $4^{th}$ graders. After the lesson, we reviewed and analyzed their worksheets and test results for examining the effects by teaching methods. Based on the result, we discussed and made some didactical suggestions for teaching the classification of triangles by angles.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.313-330
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• 2015

The classification is an important activity that is directly related to concept formation. Thus it will need to be made meaningful learning to classification through learner-centered teaching. But we doubts weather teaching and learning to the classification are reflected in the constructivist philosophy of 'learner-centered' well or not. The purpose of this study was to analyze critically the content of elementary textbooks and guidebook for teachers relating to the classification of angles and triangles in terms of constructivism. As a result, there is a problem in the classification of angles that are not provided a reasonable chance to set criteria by agreement of the communities. There is a problem in the classification of triangles that has the characteristics of radical development in terms of diversity. In addition, response of students was predicted like anyone who already acquired knowledge. And it has the shortcomings that the opportunity to have a choice and a discussion to hierarchical and partition classification are not provided. The followings are proposed based on such features; faithful reflection of 'Learner-centered' principle, careful prediction of student response, teaching that focus on process than results.

• Education of Primary School Mathematics
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• v.18 no.1
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• pp.45-59
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• 2015

This study focused on the classification of triangles by angles in elementary school mathematics. We examined Korean national mathematics curriculum from the past to the present. We also examined foreign textbooks and the Euclid's . As a result, it showed that the classification is not indispensable from the mathematical and the perceptual viewpoint. It is rather useful for students to know the names of triangles when studying upper level mathematics in middle and high schools. This study also suggested that the classification be introduced in elementary school mathematics in the context of reasoning and inquiring as shown foreign textbooks, and example topics for the reasoning and inquiring.

• The Mathematical Education
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• v.53 no.3
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• pp.383-397
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• 2014

This study aims to explore secondary students' thinking while doing proof in geometry. Two secondary students were interviewed and the interview data were analyzed. The results of the analysis suggest that the two students similarly showed as follows: a) tendencies to use the rules of congruent and similar triangles to solve a given problem, b) being confused about the rules of similar and congruent triangles, and c) being confused about the definitions, partition and hierarchical classification of quadrilaterals. Also, the results revealed that a relatively low achieving student has tendency to rely on intuitive information such as visual representations.

• International Journal of Advanced Culture Technology
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• v.10 no.3
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• pp.77-84
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• 2022

This study focused on the spirit to becoming the true "I" as a human, and it attempted to pay attention to the "images" sent by the unconscious to prompt the reality of that spirit. The purpose of this study was to identify the symbols in myths and folk tales that appeared in the individual's dreams and to shed light on how the universal experiences of humankind are re-experienced and integrated into an individual's life. This study used a total of 105 mandala paintings collected through the researcher's own dreams from February 2019 to September 2020. Among them, repeated symbols were classified into basic shapes, squares, crosses, triangles, circles, and spirals, as suggested by Riedel. The study truthfully described the discovery of a practical layer of psychology as a human's individualization and changing, resulting in autoethnography, which is a type of qualitative study.

• Education of Primary School Mathematics
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• v.24 no.4
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• pp.233-246
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• 2021

Two-dimensional shapes have a great influence on elementary school students' learning and are closely related to other content areas. Therefore, in this study, The Teaching and Learning Elements that should be taught in two-dimensional shapes were extracted from the literature. It also was analyzed that revised mathematics textbooks in the year 2015 were properly implemented with the teaching and learning elements. As a result of the analysis, in the case of Understanding The Concept, the activities in the textbooks are not able to recognize 2-D shapes which are focusing on shapes of the actual object. In the case of Classifying two-dimensional shapes according to the Criteria, the classification criteria were presented differently from what was learned in the previous course. In the aspect of Applying the Concept, the activities in order to Discuss two-dimensional shapes were not sufficient. Lastly, in view of the fact the 2015 revised curriculum is not considered with the relationship between two-dimensional shapes. For that reason, the following Knowing Relationships parts are insufficiently presented; Understanding the Relationship Between shapes through Definitions and Properties, Identifying the relationship between shapes throughout classification activities, and Discussing the relationship between shapes. Based on the analysis result of two-dimensional shapes, it is suggested that the finding of this research helps to enlarge the teaching methodology of triangles and provide educational perspectives for development in other shape areas.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.42 no.2
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• pp.249-256
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• 2022

Various studies are being actively conducted to show that the real-time visualization technology that combines BIM (Building Information Modeling) and AR (Augmented Reality) helps to increase construction management decision-making and processing efficiency. However, when large-capacity BIM data is projected into AR, there are various limitations such as data transmission and connection problems and the image cut-off issue. To improve the high efficiency of visualizing, a mesh optimization algorithm based on the k-nearest neighbors (KNN) classification framework to reconstruct BIM data is proposed in place of existing mesh optimization methods that are complicated and cannot adequately handle meshes with numerous boundaries of the 3D models. In the proposed algorithm, our target BIM model is optimized with the Unity C# code based on triangle centroid concepts and classified using the KNN. As a result, the algorithm can check the number of mesh vertices and triangles before and after optimization of the entire model and each structure. In addition, it is able to optimize the mesh vertices of the original model by approximately 56 % and the triangles by about 42 %. Moreover, compared to the original model, the optimized model shows no visual differences in the model elements and information, meaning that high-performance visualization can be expected when using AR devices.

• Journal of the Korean Society of Clothing and Textiles
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• v.40 no.1
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• pp.97-113
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• 2016

This study develops pant patterns using body shape, measurement and shell mesh data to decide optimal women's pants according to styles with excellent size, fit and shape for different individuals and silhouettes. Standard landmarks, lines, triangles and structures were set on a 3D scanned lower body shell to represent women in their twenties and flattened as a 2D pattern. Patterns were created and analyzed according to culotte, formal, slacks and tight type considering crotch shape, location of the crotch point, and adjusting waist darts. Flattened patterns were rotated to compare existing methods. The crease lines were then set through the hip protrusion point and compared. The main factor of the pant pattern were extracted, total rise, crotch depth, crotch width, angle of center line, shape of the center line curve, the thigh width, the amount of waist dart, and crease line position. With going tight style from the culotte, the fits are closer to the figure with minimized thigh circumference, the dart amount decreases, the crotch depth increases, the crotch extensions were shorter, and the angle of the center back increased. The total rise is U shape for culotte and is closer to V shape as the silhouette tightens. T-test of appearance evaluation of the developed pant pattern were conducted after analyzing measurements and shapes of each styles. The results of the developed patterns were superior to existing patterns in accordance to hip line between body and pants as well as appearance evaluation. We found systematic mechanisms among pattern factors that create various pant silhouettes. Evidence on classification of the silhouettes of traditional types of pants were explained objectively through the process of playing out 3D forms.

• Education of Primary School Mathematics
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• v.20 no.2
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• pp.163-175
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• 2017

The purpose of the study is to identify the effect of length and right angle indication on the understanding of the concept of the figure when presenting the task of classifying the plane figures. we recorded thirty three 4th grade students' performance with eye-tracking technologies and analyzed the correct answer rate and gaze duration. The findings from the study were as follows. First, correctness rate increased and Gaze duration decreased by marking length in isosceles triangle and equilateral triangle. Second, correctness rate increased and Gaze duration decreased by marking right angle in acute angle triangle and obtuse triangle. Based on these results, it is necessary to focus on measuring the understanding of the concept of the figure rather than measuring the students' ability to measure by expressing the length and angle when presenting the task of classifying the plane figures.